Answer
$$B = 20.6^\circ ,\,\,\,C = 116.9^\circ ,\,\,\,c = 20.6{\text{ft}}$$
Work Step by Step
$$\eqalign{
& A = {\text{42}}.{\text{5}}^\circ ,a = {\text{15}}.{\text{6 ft}},b = {\text{8}}.{\text{14 ft}} \cr
& {\text{Use the law of sines to find the angle of }}B \cr
& \frac{{\sin B}}{b} = \frac{{\sin A}}{a} \cr
& \sin B = \frac{{b\sin A}}{a} \cr
& {\text{Substituting }} \cr
& \sin B = \frac{{\left( {{\text{8}}.{\text{14}}} \right)\sin \left( {{\text{42}}.{\text{5}}^\circ } \right)}}{{{\text{15}}.{\text{6}}}} \cr
& {\text{Use a calculator}} \cr
& \sin B \approx 0.3525195058 \cr
& B \approx {\sin ^{ - 1}}\left( {0.3525195058} \right) \cr
& B \approx 20.6^\circ \cr
& \cr
& {\text{Calculate the angle of }}C \cr
& C = 180^\circ - A - B \cr
& C = 180^\circ - {\text{42}}.{\text{5}}^\circ - 20.6^\circ \cr
& C = 116.9^\circ \cr
& \cr
& {\text{Use the law of sines to find side }}c \cr
& \frac{c}{{\sin C}} = \frac{a}{{\sin A}} \cr
& c = \frac{{{\text{15}}.{\text{6}}\sin \left( {116.9^\circ } \right)}}{{\sin \left( {{\text{42}}.{\text{5}}^\circ } \right)}} \cr
& c \approx 20.6{\text{ft}} \cr
& \cr
& {\text{Answer}} \cr
& B = 20.6^\circ ,\,\,\,C = 116.9^\circ ,\,\,\,c = 20.6{\text{ft}} \cr} $$
